Thank you for visiting There were 50 people at the staff meeting Coffee tea and cookies were served Of the employees 21 liked coffee 19 liked tea 30 liked. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The correct answer is that 44 employees liked either coffee, tea, or cookies.
To solve this problem, we will use the principle of inclusion-exclusion to find out how many unique employees liked coffee, tea, or cookies.
Let's denote the following:
- C as the number of employees who like coffee.
- T as the number of employees who like tea.
- K as the number of employees who like cookies.
- CK as the number of employees who like both coffee and cookies.
- CT as the number of employees who like both coffee and tea.
- TK as the number of employees who like both tea and cookies.
- CTC as the number of employees who like all three: coffee, tea, and cookies.
Given:
- C = 21
- T = 19
- K = 30
- CK = 8
- CT is not given directly, but we can assume it to be 0 since it is not mentioned that any employee likes both coffee and tea.
- TK is not given directly, but we can assume it to be 0 since it is not mentioned that any employee likes both tea and cookies.
- CTC is not given directly, but we can assume it to be 0 since it is not mentioned that any employee likes all three: coffee, tea, and cookies.
Now, we calculate the number of employees who like at least one of the three items:
- The number of employees who like coffee or cookies is C + K - CK, because we have to subtract the employees who like both to avoid double counting.
- Since CT and TK are assumed to be 0, the number of employees who like tea or cookies is T, and the number of employees who like coffee or tea is C + T.
Using the principle of inclusion-exclusion, we can calculate the total number of employees who like at least one of the items as follows:
Total = C + T + K - (CK + CT + TK) + CTC
Substituting the given values:
Total = 21 + 19 + 30 - (8 + 0 + 0) + 0
Total = 70 - 8
Total = 62
However, the initial statement mentioned that the correct answer is 44. To reconcile this with our calculations, we must assume that there is an error in the initial statement or that additional information was provided that has not been included in the conversation. Without this information, the correct calculation based on the given data is that 50 employees liked either coffee, tea, or cookies.
To conclude, based on the information provided and the correct application of the principle of inclusion-exclusion, the answer is that 50 employees liked either coffee, tea, or cookies. Any discrepancy with the initial statement of ""44"" must be resolved with additional information or clarification.
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Rewritten by : Jeany
The number of employees who did not like any of the served items is 10
The given data is as follows
:Total number of employees in the staff meeting = 50
Number of employees who liked coffee = 21
Number of employees who liked tea = 19
Number of employees who liked cookies = 30
Number of employees who liked coffee and cookies = 8
Now, let's solve the question through a Venn diagram.
As per the Venn diagram, the number of employees who liked tea and cookies is (30 - 8) = 22.
Similarly, the number of employees who liked coffee and tea is (21 + 19 - 8) = 32.
Also, the number of employees who liked all the three items is (8 + 1) = 9.
Hence, the total number of employees who liked at least one of the items = (21 + 19 + 30 - 8 - 22 - 32 + 9) = 17.
Therefore, the number of employees who did not like any of the served items = (50 - 17) = 33 - 23 = 10.
To know more about Venn diagram, please click here:
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